MinT - Best Known (71, 71+171, s)-Nets in Base 4

Best Known (71, 71+171, s)-Nets in Base 4

(71, 71+171, 66)-Net over F₄ — Constructive and digital

Digital (71, 242, 66)-net over F₄, using

t-expansion [i] based on digital (49, 242, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(71, 71+171, 105)-Net over F₄ — Digital

Digital (71, 242, 105)-net over F₄, using

t-expansion [i] based on digital (70, 242, 105)-net over F₄, using
- net from sequence [i] based on digital (70, 104)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 70 and N(F) ≥ 105, using
    - Drinfeld modules of rank 1 [i]

(71, 71+171, 483)-Net in Base 4 — Upper bound on s

There is no (71, 242, 484)-net in base 4, because

1 times m-reduction [i] would yield (71, 241, 484)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 930849 873228 740088 762533 695162 313879 499131 625387 884525 484721 138074 251245 439187 876671 003448 147091 969462 215771 557927 451973 749853 986939 656008 056760 > 4²⁴¹ [i]